Higher-order Skyrme hair of black holes

Abstract

Higher-order derivative terms are considered as replacement for the Skyrme term in an Einstein-Skyrme-like model in order to pinpoint which properties are necessary for a black hole to possess stable static scalar hair. We find two new models able to support stable black hole hair in the limit of the Skyrme term being turned off. They contain 8 and 12 derivatives, respectively, and are roughly the Skyrme-term squared and the so-called BPS-Skyrme-term squared. In the twelfth-order model we find that the lower branches, which are normally unstable, become stable in the limit where the Skyrme term is turned off. We check this claim with a linear stability analysis. Finally, we find for a certain range of the gravitational coupling and horizon radius, that the twelfth-order model contains 4 solutions as opposed to 2. More surprisingly, the lowest part of the would-be unstable branch turns out to be the stable one of the 4 solutions.

LaTeX: 51 pages, 21 figures; V2: references added and typos corrected

References in corpus (8)

• BPS Skyrmions as neutron stars
• Spinning Gravitating Skyrmions
• Topological solitons in the supersymmetric Skyrme model
• Skyrmions, Skyrme stars and black holes with Skyrme hair in five spacetime dimension
• A higher-order Skyrme model
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Cited by in corpus (3)

• Skyrmions around Kerr black holes and spinning BHs with Skyrme hair
• Neutron stars within the Skyrme model
• Gravitating gauged BPS baby Skyrmions